The common name exists for the pretty obvious reason that the buds enlarge like blue balloons before the petals open up. The Latin prefix, platy-, means broad (think of the broad beak of the Platypus). In this case, the root word refers to the plants' broad petals.

Finally, I am including a favorite annual, Gomphrena globosa, or Globe Amaranth:

Note that the pink 'petals' are really bracts and the true flower is tiny and white and sits among the many bracts.